The following is a example of what high velocity guns hitting percentages are at 'short' battlefield ranges:

Scenario A Hetzer unit, the first fielded in the East, is in a battle within a large city and must defend against all armor penetrating into the main city area. The main street is 400 meters long and flat. The Hetzer unit have been issued a limited number of APCR rounds to ensure that their combat debut is successful.

Upon arriving in the city, they are warned by the infantry in regards to Soviet Tanks already in the main square up the 400 meter street. The first Hetzer enters the road and turns and faces a Soviet tank several hundred meters up the road directly facing him.

The commander has no time to judge the range and orders "Zone 1, APCR, FIRE!". The gunner immediately sets the elevation to 0.1 degrees, puts his aiming mark at the center of the Soviet tank and fires.

The attached drawing illustrates the following:

Black ellipse is the triple dispersion area (3 x 50% zone of dispersion) for the APCR round if, indeed, the enemy tank is 300 meters away.

Green ellipse shows the triple dispersion area is the enemy tank is 400 meters away. Note it is a larger dispersion and also wider.

The red ellipse is actually the dispersion about the highest point the APCR round would have flown. It is about 150 meters. In other words, any enemy tank between the Hetzer and up to 400 meters has a great probability of being hit.

The triple dispersion of the 50% dispersion gives the area that 99% of the rounds will land.

Another way to look at this data is to apply the 'Standard Range Estimation Percentage Errors'. If the method was to guess the range, then even a 33% range guestimation-error would have little impact. A very high percentage of hits would occur on first round shots. In fact, even if the target tank were 500 meters, then the 'green dispersion ellipse' would sink further down, but it would still overlay the target. A 50% probability of hitting the lower front might be possible.

Range estimation errors are more a function of range. I was in tehe Army and had LAW training and we were taught to use an extended arm with a fist to guage the range to M60 tanks. If a tank was 300 meters away, I could estimate it's range to within 50 meters.

An observation on the dispersion in the drawing...once dispersion is as tight as the black ellipse, then targetting areas of the tank become possible (on a stationary target). Going for a turret shot or the drivers hatch or a track becomes statistically do-able.

No, the formula in their book. It spells out a theoretical hit percent based on range estimation error and gun dispersion. That is what I primarily use in my ballistic model. (Plus a few other modifications.)

Here is a diagram of the Bird-Livingston ranging estimation error for 25% ranging error. (I blurred up the image as it is copyrighted and they might republish their book.)

The lower diagram is my take on the formula. The problem I found is that it pings on the 100% level at around the 350 meter range. Like your diagram with the T-34/85 the dispersion is less than the height or width of the target so theoretically it is impossible to miss even with a ranging error. To make it more realistic for the game I incorporated a human error factor so the accuracy is never 100%.

This extra error could include parallax and what the British call jump and throw-off.

The tactic of firing by zones could, of course, be extended to the 'next zone'. That is, 'Zone 2' might extend from 400-750 meters. The zones would naturally be shorter as they are progressed. This is due to the squared effect of gravity. The basic benefit of this system is a better assurance of first round hits in a timely manner. Overlap of the zones, due to higher velocity and flatter trajectory, allows even a panicky crew to have some chance at success. Basically, at short battlefield distances, AT weapons with a high velocity like the German APCR round, the first round hit percentages would be higher than the graphs show as far as 500-750 meters range. A weapon like the Panther gun, which is in this velocity range for its AP39 round, would be a more common example. I have seen the APCR production numbers for both KWK/StuK 40 and PAK 40 weapons. It's actually lower than people think. Mostly because the 'W' (soft) rounds seemed to have been counted in.

I have seen one source that claims APCR for the KWK/SuK 40 guns was nothing more than 30,000 for the tungsten and about twice as many for the 'W' soft rounds. Production halted in August 43 and stocks were very low at the end of the year. Maybe 17,000 combined APCR+W rounds for the L48 guns. Most large caliper weapons like the 88s had the rounds recalled. There were a lot more smaller caliber rounds especially 50mmL42 and 37mm but these really sucked against sloped armor.

The PAK40 had a similar yet smaller number made.

This is supposedly usage numbers but I suspect they are manufacturing data.

It would probably be clearer if you tried to overlap the dark blue ellipse over my green (400m) ellipse. Also, overlap the lt. blue over my black (300m).

Mobius -> RE: High Velocity AP round hit-zones (12/1/2012 4:50:23 PM)

I'm re-reading the Bird-Livingston formula and it says the std dev is from the aim point. That would make the 50% zone also measured from the aim point. That would put my ellipses at twice the size. I was assuming the 50% zone and std dev to be the size of a box about the aim point. The evidence for this would be the 88mm Flak firing table which where the 50% Dispersion has height and width columns.

Not sure if we are on the same page, but tell me if you agree with this drawing.I wanted to do this with 1000m data but used 800m by mistake. In any case, the actual ovals/circles convey what the 50% data and 3X data and also the one std. dev. means to me. I am remembering discussing this type of data with Rexford and the implications of using Double Dispersion.

The scale is off but I am just trying to convey the idea. Mostly, in order to zero a gun, there must be sufficient accuracy. Even with t6he accuracy that is shown here, zeroing might take a dozen or so rounds.

From what I'm finding now is that the 50% width should be divided by 2 to find the horizontal dispersion from the aim point. Then that number divided by .67448 to get 1 std dev from the aim point. (Similarly the 50% height should be divided by 2 then divided by .67448 to get the vertical dispersion.) 3 x that distance from the aim point would include 99.72% of possible hits. It looks like Bird (Rexford) wrote such in a post in 2000. But in his book the example he gives with the 88mm at 800m (pages 95-96) it seems he left out the divide by 2 part.

quote:

Note: At 800m range, 50% of the rounds fired at a constant aim will be within a box... 88L56 APCBC 800m....0.3m/0.2m

In the book the SD of the vertical dispersion of the 88mm@800m is given as 0.44. But 0.3m/2 = 0.15m, 0.15m/.67448 =0.222m <> 0.44m Likewise in the book example the sd of the horizontal dispersion is given as 0.3m. But 0.2m/2 = 0.1, 0.1/.67448 = 0.148m. Not 0.3m.

To convert to normal distribution, see attached graph. convert the one side of bell curve as follows...

Relate half side of 0.4m converts to 0.2m (divide by two). Red line under graph shows line that is related to yellow cumulative percentage on bottom and total length of red line is 0.4m. This is then 25%. Relate 25% to 19.1% (0.5 of Z score). This is 0.1528m.

0.2mx(.191/.25)=0.1528m

This is then multiplied by 6 to get 99% or multiplied by 5 to get 96%. Note this is just one side of distribution. As per the example, it would be 0.9168 below the Bell Curve and 0.9168 above. This would make 99% dispersion 1.833m on a vertical target at 800m. At 1000m, with a vertical dispersion of 50% and 0.6 meters, it really gets larger than a standard 2m by 2.5m target. Zeroing would be questionable.

And it checks very well with the 'tripling of the 50%' data. At two sigma, they are the same. I should revise the graphic to show the zones.

But the normal distribution, and even my 'tripling of 50%', are assuming that things are conforming to math. It should be the other way around. The only real data to be had is the 50% data in the German documents. Where the other 50% land is not spelled out.

I have read that the Germans would take the horizontal and vertical components from each shot. That is, they measured how far away the shot landed away from the aimed point of impact. They probably added up the X data and Y data and divided by the number of shots. This is the data I would like to see.

I don't think a model that uses a 3 sigma approach is valid unless there is data to support it. As a educated guess, 2.5 sigma is more realistic.

I was just looking at that data on lonesentry. Maybe a misprint? 1,200 yds?

Mobius -> RE: High Velocity AP round hit-zones (12/3/2012 4:03:36 AM)

Looking at some of these old posts I find some where Lorrin is saying to use half the 50% dimensions to get the std. dev. and others where he says to use the full value. Today I changed my ballistics program to use 1/2 the 50% zone value and it no longer produces results that match firing range tests.

Per WO 291/180 live tests of the 17 pdr my ballistic program matched accuracy within 3% at 1000yd and 0.5% at 1500yds and 1% at 2000yds. That was one reason I chose his formula, because it produced realistic results. I think I'll go back to doing it the way it is written in his book not per the 2000 BF post.

I assume this is the data: These are numbers collected by British Army Operational Research Sections during WWII (summarized in WO 291/180) Ranges are in yards, report indicates that the target is assumed to be a approximately the size of a Tiger Ie. Hit probability also assumes no crew error in line or range estimation.